Quantum-induced interactions in the moduli space of degenerate BPS domain walls
Field Theories in Lower Dimensions
Solitons Monopoles and Instantons
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[EN] In this paper quantum eﬀects are investigated in a very special two-scalar ﬁeld model having a moduli space of BPS topological defects. In a (1 + 1)-dimensional space-time the defects are classically degenerate in mass kinks, but in (3 + 1) dimensions the kinks become BPS domain walls, all of them sharing the same surface tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum kink and domain wall ﬂuctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to accommodate the infrared divergences due to zero modes in the spectra of the second-order kink and domain wall ﬂuctuation operators, which are respectively N ×N matrix ordinary or partial diﬀerential operators. Use of these tools in the spectral zeta function associated with the Hessian operators paves the way to obtain general formulas for the one-loop kink mass and domain wall tension shifts in any (1 + 1)- or (3 + 1)-dimensional N-component scalar ﬁeld theory model. Application of these formulae to the BPS kinks or domain walls of the N = 2 model mentioned above reveals the breaking of the classical mass or surface tension degeneracy at the quantum level. Because the main parameter distinguishing each member in the BPS kink or domain wall moduli space is essentially the distance between the centers of two basic kinks or walls, the breaking of the degeneracy amounts to the surge in quantum-induced forces between the two constituent topological defects. The diﬀerences in surface tension induced by one-loop ﬂuctuations of BPS walls give rise mainly to attractive forces between the constituent walls except if the two basic walls are very far apart. Repulsive forces between two close walls only arise if the coupling is approaches the critical value from below.
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